Temperature Measurement Gerald Recktenwald, Evan Thomas Portland State University Department of Mechanical Engineering

Temperature Measurement • Liquid bulb thermometers • Gas bulb thermometers • bimetal indicators • RTD: resistance temperature detectors (Platinum wire) • thermocouples • thermistors • IC sensors • Optical sensors ⊲ Pyrometers ⊲ Infrared detectors/cameras ⊲ liquid crystals

IC Temperature Sensors • Semiconductor-based temperature sensors or thermocouple reference-junction compensation • Packaged suitable for inclusion in a circuit board • Variety of outputs: analog (voltage or current) and digital • More useful for a manufactured product or as part of a control system than as laboratory instrumentation.

Thermistors A thermistor is an electrical resistor used to measure temperature. A thermistor designed such that its resistance varies with temperature in a repeatable way. A simple model for the relationship between temperature and resistance is ΔT = kΔR A thermistor with k > 0 is said to have a positive temperature coefficient (PTC). A thermistor with k < 0 is said to have a negative temperature coefficient (NTC). Photo from YSI web site: www.ysitemperature.com

Thermistors Advantages • Output is directly related to absolute temperature - no reference junction needed. • Relatively easy to measure resistance • Sensors are interchangeable (±0.5◦C) Disadvantages • Possible self-heating error ⊲ Each measurement applies current to resistor from precision current source ⊲ Measure voltage drop ΔV , then compute resistance from known current and ΔV . ⊲ Repeated measurements in rapid succession can cause thermistor to heat up • Can be more expensive than thermocouples for comparable accuracy: $10 to $20/each versus $1/each per junction. Thermistors costing less than $1 each are available from electronic component sellers, e.g. Digikey or Newark. • More difficult to apply for rapid transients: slow response and self-heating

Thermistors Calibration uses the Steinhart-Hart equation 50 Data Calibration uses the Steinhart-Hart equation 45 Curve Fit 40 35 30 25 Nominal resistance is controllable by manufacturing. 20 15 Typical resistances at 21◦C: 10 10 kΩ, 20 kΩ, . . . 100 kΩ. 5 5 10 15 20 25 30 Resistance (kΩ)

Thermistors Ohmmeter Two-wire resistance measurement: Resistance in the lead wires can lead to inaccurate temperature measurement. Ohmmeter Thermistor I RT V

Thermistors Four-wire resistance measurement eliminates the lead resistance1 Ohmmeter Rlead Thermistor Rlead I RT V Rlead Rlead 1Sketch adapted from Hints for Making Better Digital Multimeter Measurements, Agilent Technologies Corporation, www.agilent.com.

Thermocouples Metal A VAB Metal B Heat + - Type K • Principle of operation • Wire types: B, E, J, K, N, R, S, T • Formats: prefab, homemade, fast response, slow response • Circuit diagrams: reference junction compensation • Good practice Metal A + VAB Metal B - Heat Type K Chromel {90% nickel and 10% chromium} Alumel {95% nickel, 2% manganese, 2% aluminum and 1% silicon} 41 µV/°C −200 °C to +1350 °C / -330 °F to +2460 °F range.

Seebeck Effect E12 = σ(T2 − T1) Temperature gradient in a conductor induces a voltage potential T2 E12 Voltmeter T1 E12 = σ(T2 − T1) (1) where σ is the average Seebeck coefficient for the range T1 ≤ T ≤ T2.

Seebeck Effect Perturb T2 while holding T1 fixed: (2) Subtract Equation (1) from Equation (2) to get (3) Rearrange (4) σ is an intrinsic property of the material, so (5)

Seebeck Effect Applying the limit yields the derivative: so (6) Equation (6) is the definition of the Seebeck Coefficient Nominal values of Seebeck Coefficient σ values are small, so the voltage output from thermocouples is small, typically on the order of 10−3 V.

Reference Junction Thermocouples are only capable of measuring temperature differences. Physical Circuit: x Tt Tr To measure the temperature of an object, we need a known reference temperature. The thermocouple is used to measure the temperature difference between the object and the known reference temperature. material P Tj 1 Cu 2 Voltmeter 3 5 Cu 4 material N Conceptual T(x) Plot: Tj 3 Ejr emf relative to reference junction Tt 1 5 Etr Cu Cu Tr 2 4 x

Ice Point Reference Junction Ice-point reference junction used in the thermal lab: Glass tube, partially filled with oil Ice/water mixture Insulated thermos

Calibration Curves Working with calibration data • Integrals are never evaluated. Calibration data for T-Type thermocouples: E (mV) T (◦C) 0.0000 0 • Data is tabulated and curve fit • Standard polynomial curve fits and coefficients are available for common thermocouple types 2.0357 50 4.2785 100 6.7041 150 9.2881 200 12.0134 250 14.8619 300 17.8187 350 20.8720 400

Temperature Data Acquisition and Analysis Evan Thomas Portland State University Department of Mechanical Engineering

The first is a business model – using carbon credits that are generated from the projects themselves and sold to international buyers, to close the loop on funding. The second is a tech solution – using cellular network based remotely reporting sensors to tell us how projects are performing around the world.

Analog to Digital Conversion Resolution – the number of bits involved in an analog to digital conversion. Conversion time – the time it takes for an ADC to convert an analog voltage sample to a digital code. Quantization error – The rounding error between the true analog value and the recorded digital value. Voltage 2-Bit Digital Representation 0 to 2.5 00 2.5 to 5 01 5 to 7.5 10 7.5 to 10 11

Digital Data Hexadecimal numbers Signing bit Save space Represent negative numbers Known as twos complement Decimal Hexadecimal 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 F Bits Unsigned value 2's complement value 0111 1111 127  127  0111 1110 126  126  0000 0010 2  2  0000 0001 1  1  0000 0000 0  0  1111 1111 255  −1  1111 1110 254  −2  1000 0010 130  −126  1000 0001 129  −127  1000 0000 128  −128 

Digital Data

R Project The R Project for Statistical Computing is a free, open source and powerful statistically, analysis and plotting software program. It can perform many of the tasks of Excel, Stata, MatLab and SAS, and integrate with many other systems including online datasets and MySQL databases. In this lab, we will use R to: Download data from MySQL data tables Import data from lab calibration runs Plot data Derive calibration curve